Law of Sines Formula
The law of sines formula is used for relating the lengths of the sides of a triangle to the sines of consecutive angles. It is the ratio of the length of the side of the triangle to the sine of the angle thus formed between the other two remaining sides. The law of sines formula is explained below with the following solved examples.
What is the Law of Sines Formula?
The law of sines formula is used for any triangle apart from SAS triangle and SSS triangle. It says:
a/ sin A = b/ sin B = c/sin C
Where
 a, b, and c are the lengths of the triangle
 A, B, and C are the angles of the triangle.
Let us see the applications of the law of sines formula in the following solved examples.
Solved Examples Using Law of Sines Formula

Example 1: For a triangle, it is given a = 20 units c = 25 units and angle C = 42^{∘}. Find the angle A of the triangle.
Solution:
To find: Angle A
Given:
a = 20, c = 25, and angle C = 42^{∘}.
Using law of sines formula,
a / sinA = b / sinB = c / sinC
20 / sinA = 25 / sin 42
sinA = 0.8363
∠A = 56.7^{∘}
Answer: ∠A = 56.7^{∘}

Example 2: It is given ∠A = 47^{∘}, ∠B = 78^{∘}, and the side c = 6.3. Find the length a.
Solution:
To find: Length of a
Given:
∠A = 47^{∘}, ∠B = 78^{∘}, and c = 6.3.
Since, the sum of all the interior angles of the triangle is 180^{∘, }
Therefore,
∠A + ∠B + ∠C=180^{∘}
47^{∘ }+ 78^{∘ }+ ∠C=180^{∘}
∠C = 55^{∘}
Using law of sines formula,
a / sinA = b / sinB = c / sinC
a / SinA = c / SinC
a / Sin47^{∘ }= 6.3 / Sin55^{∘}
a = 6.3 / Sin55^{∘ }× Sin47^{∘}
a = 5.6
Answer: a = 5.6